Runoff modelling of the Mara River using satellite observed soil moisture and rainfall

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

JONATHAN MUITHYA MWANIA March, 2014

SUPERVISORS:

Dr. Ir. Rogier van der Velde

Dr. Zoltan Vekerdy

Thesis submitted to the Faculty of Geo-Information Science and Earth Observation of the University of Twente in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation.

Specialization: Water Resources and Environmental Management

SUPERVISORS:

Dr. Ir. Rogier van der Velde Dr. Zoltan Vekerdy

THESIS ASSESSMENT BOARD:

Prof. Dr. Ing. W. Verhoef (Chair)

Dr. H. van der Kwast (External Examiner, UNESCO-IHE Delft)

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

JONATHAN MUITHYA MWANIA

Enschede, The Netherlands, March, 2014

DISCLAIMER

This document describes work undertaken as part of a programme of study at the Faculty of Geo-Information Science and Earth Observation of the University of Twente. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the Faculty.

ABSTRACT

Hydrological models are necessary tools in water resource management. However modeling in poorly gauged catchments is a big challenge. Recent research has shown that satellite based hydrological and meteorological data has the potential of being part of the solution towards overcoming this challenge. In this research we use the conceptual lumped rainfall-runoff model by Meier et al. (2011) to model runoff in the Mara River Basin. The model simulates runoff as a function of soil moisture with runoff as forcing data. It is built on the basis established between satellite observed soil moisture and rainfall, and the measured runoff. Reliability of the model is evaluated over three sub-catchments namely Mara mines, Nyangores and Amala in the Mara river basin using correlation coefficient (r) and Root Mean square Errors (RMSE) Mean Absolute Error and bias. The r for Mara mines Nyangores and Amala during calibration and (validation) were 0.54 (0.77), 0.67 (0.74), 0.125 (0.48) respectively. The model showed great potential in simulating dry season runoff. It needs further improvement to be able to fairly simulate wet season runoff.

Key words: Hydrological modeling, soil moisture, rainfall, runoff

ii

To God be the Glory

ACKNOWLEDGEMENTS

First I wish to express my appreciation to the Dutch government for offering me the NFP (Netherlands Fellowship Program) scholarship. If it was not for the scholarship, it would have been impossible to do the Master of Science Program in the Netherlands. On the same note I wish to express my appreciation to the ESA (European Space Agency) Tiger Initiative - Alcantara Project for partially funding the fieldwork of this research.

Second I wish to express my heartfelt gratitude to my supervisors, Dr. Ir. Rogier van der Velde and Dr.

Zoltan Vekerdy for their unrelenting support and critical review of this work. Particularly I thank Dr. Ir.

Rogier van der Velde for sharing with me the journal article containing the model concept used in this research and computer codes for data pre-processing. I thank Dr. Zoltan Vekerdy for facilitating my fieldwork and the extra efforts of providing leadership and capturing the fieldwork moments in pictures. I wish to thank Joseph Mtamba of the University of Dar Salaam, the Principal Investigator (PI) for being very supportive and listening during my many consultations with him. Gentlemen thank you for the excellent mentorship.

I wish to thank Drs Robert Becht for providing a link to Professor M. E. McClain of UNESCO – IHE (Institute for Water Education) from whom I obtained historical discharge data for the MRB. Kind regards to Mr Richard Kidd of TU Wien (Vienna University of Technology) for providing me with information on downloading the satellite observed soil moisture data used in this research. Kind regards also to the soil laboratory staff of the University of Dar Salaam Dar Salaam for analyzing the soil samples collected during fieldwork.

I take this opportunity to also thank the chairman of Amala river branch of the Mara River Water Users Association (MRWUA) Mr Joseph Chepusit and vice-chair Madam Jessica Tesot for showing us around the upper and middle parts of the MRB and for sharing information on the role of MRWUA as a key stakeholder in the management of the basin.

I wish to thank Mr Reuben Ngessa of Water Resources Management Authority (WRMA) for facilitating my access to recent discharge data of Amala and Nyangores rivers. On the same note I thank Kenya Meteorological Department (KMD) for providing measured rainfall data used in this research.

I wish to thank the staff at the Department of Water Resources at Faculty of Geo-Information Science and Earth Observation of the University of Twente for building me professionally. I am also very grateful to my classmates for the social and moral support during the period we have been together.

Last but not the least I wish to express my heartfelt gratitude to my family and in particular my wife

Enessia for providing me with the much needed encouragement and moral support. She took excellent

care of our two sons, Luckwell and Mwanga in my absence.

iv

TABLE OF CONTENTS

1. Introduction ... 11

1.1. Background ... 11

1.2. Problem statement ... 12

1.3. Objectives ... 13

1.4. Research questions ... 13

2. Study area and data collection ... 14

2.1. Study area ... 14

2.2. Ground measurements and field observation ... 14

2.3. Satellite data sets ... 17

3. SWI, runoff, Rainfall Time series analysis ... 21

3.1. BWI and TRMM rainfall relationship ... 22

3.2. BWI and runoff relationship ... 23

3.3. TRMM rainfall versus in situ measured rainfall ... 23

3.4. Water budgets at Mara mines, Amala and Nyangores ... 25

4. Rainfall-Runoff model ... 27

5. Model performance ... 29

5.1. Calibration and Sensitivity Analysis ... 29

5.2. Validation ... 32

5.3. Long term runoff simulations ... 33

5.4. Error analysis ... 34

6. Discussion ... 36

7. Final remarks ... 38

7.1. Conclusions ... 38

7.2. Recommendations ... 38

LIST OF FIGURES

Figure 1: The picture on the left shows a man cutting trees in the upper Mara River Basin. The picture on the right shows men washing motorbikes and few steps down stream, cattle drinking the turbid water.

Human activities are contributing to degradation of the basin. Pictures by Vekerdy Z. (2013) ... 12 Figure 2: Map of the MRB. The major land covers/uses in the basin include forest reserves on the upper northern parts, in the middle parts are the savannah vegetation supporting the Mara-Serengeti ecosystem.

In the lower southern parts is Mara wetlands. Source: Dessu & Mellesse (2012)... 14 Figure 3: The picture on the left is Amala RGS at Kapkimolwa, Mulot. The station was rehabilitated and equipped with an automatic gauge with support from the World Bank Nile Basin Initiative (WB-NBTF), Swedish International Development Cooperation Agency (SIDA) and the Germany Society for

International cooperation (GIZ). The picture on the right is neglected RGS at Emarti bridge along the Amala river. Picture by: Vekerdy Z. (2013). ... 15 Figure 4: Weather station at the Mara River Water Users Association (MRWUA) office in Mulot. The station has a tipping bucket and a manual rain gauge. The weather station automatic measuring

instruments are not yet connected to the data logger. Picture by Vekerdy Z. (2013) ... 16 Figure 5: Soil Map of the MRB extracted from the HWSD raster map. The sampling points for this research are also shown in the map. ... 20 Figure 6: Processed SRTM DEM illustrating the elevation of MRB. The figure also shows the RfGS used in this research and RGS along the MR ... 20 Figure 7: BWI, TRMM and discharge 30 day daily mean time series plots for Mara mines, Nyangores and Amala sub catchments. BWI is expressed as a percentage on the right Y axis together with rainfall in mm while runoff is on the left scale. Nyangores and Amala have relatively higher BWI compared to Mara mines. The peaks tend to follow a seasonal pattern. The peak rainfall seasons in MRB are March to May and November to December. ... 21 Figure 8: BWI versus TRMM scatter plots for Mara mines, Nyangores and Amala sub catchments. The plots are for 30 day daily means. The slope is taken as an indicator of the infiltration rate of the given catchment. A steep slope indicates higher infiltration rate and vice versa. Mara mines is shown to have the lowest infiltration rate compared to Nyangores and Amala. The study period was between January 2007 and July 2013. ... 22 Figure 9: Runoff versus BWI scatter plots for Mara mines, Nyangores and Amala sub catchments. The plots are for 30 day daily means. The steepness of the slope is taken to indicate the water storage capacity of the catchment. A steep slope indicates low catchment storage capacity and vice versa. Nyangores is shown to have the highest storage capacity. The study period was between January 2007 and July 2013. . 23 Figure 10: TRMM versus in-situ measured rainfall for selected RfGS scatter plots. The data plotted is pixel (TRMM) to in-situ measurements computed to 30 day summations. The solid line represents the linear relationship of TRMM and in-situ measurement while the dotted line represents a 1:1 linear relationship.

The period for the investigation was between January 2007 and July 2013. ... 24

Figure 11: Monthly mean runoff for Nyangores and Amala rivers for the period 1964 to 1992. The Amala

River has higher and early peak runoff compared to Nyangores. The latter however has higher base flow

... 25

Figure 12: The input in this set up is rainfall. The level of BWI determines the distribution of rainfall

between the surface and subsurface storage compartment. As the BWI increases, infiltration reduces and

more rainfall is routed to the surface storage. The two storage compartments contribute to surface and

groundwater runoff. Source: Meier et al. (2011) ... 28

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Figure 13: Sensitivity analysis results. The dotted vertical line indicates the initial values of the 

parameters and time lags τ and τ

. Only 

was found to be sensitive. 

and 

were equated to 1 and 

to zero. ... 30 Figure 14: Comparison of simulation and measured runoff during calibration results at Mara mines. (a) is simulations with 

, 

, 

and 

parameters while (b) shows simulations taking into consideration only the 

parameter. The model simulations are shown to improve with reduction of the parameters. ... 31 Figure 15: Measured and simulated runoff for Mara mines, Nyangores and Amala sub-catchments during calibration of the model with only the 

parameter. The model fairly simulates low flows than peak flows.

... 31 Figure 16: Measured and simulated runoff for Mara mines, Nyangores and Amala sub catchments during validation. The model poorly simulates quick peak runoff in Mara mines and Amala. It is also

overestimating low flows in Amala ... 32 Figure 17: Long term runoff simulations on a daily model time step for Mara mines, Nyangores and Amala sub catchments. The simulation period is from January 2007 up to July 2013. ... 33 Figure 18: Comparison of the monthly summations of simulated surface and groundwater runoff

components for Mara mines, Nyangores and Amala sub catchments. The simulation period is from

January 2007 up to July 2013. Nyangores generates the highest surface and groundwater runoff while Mara

mines generates the least. ... 34

Figure 19: Error analysis at Mara mines, Nyangores and Amala. The bias error of the simulations tends to

be propagated by intensity of the rainfall events. ... 35

LIST OF TABLE

Table 1: RGS along the Mara River. Only the Mara mines, Nyangores and Amala RGSs have relatively long historical data. ... 16 Table 2: Soil particle distribution analysis results, S Pt. is sample point, C is clay, Slt silt, Snd sand and G gravel. The samples were classified with the USDA Texture Class. ... 17 Table 3 Satellite data sources. These sources are open to the public. ... 17 Table 4: Gridded TRMM rainfall products have been spatial averaged with a resolution of 0.25° x 0.25°

and 1° x 1°. 3B42 is also available on a daily temporal resolution. Source: NASA (2011) ... 18

Table 5: SRTM DEM specifications, source: USGS (2012) ... 19

Table 6: TRMM rainfall validation with in-situ measured rainfall. The period for the investigation was

between January 2007 and July 2013. There are gaps in the in-situ measurements for all the RFGS in the

basin. ... 25

Table 7: Water budgets for Mara mines, Nyangores and Amala sub catchments. There are many gaps in

the runoff data hence these budgets are not conclusive ... 26

Table 8: Calibration results for Mara mines, Nyangores and Amala sub catchments. High 

indicates high

losses in the sub catchment and vice versa ... 30

Table 9: validation results for Mara mines, Nyangores and Amala sub catchments. Mara mines has the

lowest RMSE, MAE and bias and the highest r. ... 33

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LIST OF ABBREVIATIONS

AMSR-E Advanced Microwave Scanning Radiometer for Earth Observation System ASCAT Advanced Scatterometer

ASCII American Standard Code for Information Interchange

BWI Basin Water Index

CERES Cloud and Earth Radiant Energy Sensor DEM Digital Elevation Model

EGM96 Earth Gravitational Model 1996 ERS European Remote Sensing

ESA European Space Agency

EUMETSAT European Organisation for the Exploitation of Meteorological Satellites

FDC Flow Duration Curve

GeoSFM Geospatial Stream flow Model GeoTIFF Geo-referenced TIFF

GLDAS Global Land Data Assimilation System GRACE Gravity Recovery and Climate Experiment GSFC Goddard Space Flight Canter

GV Ground Validation

HDF Hierarchical Data Format

HWSD Harmonized World Soil Database IDL Interactive Data Language

ISBA Interaction-Soil-Biosphere-Atmosphere KMD Kenya Meteorological Department LPRM Land Parameter Retrieval Model LVB Lake Victoria basin

m.a.s.l Metres above sea level MetOp Meteorological Operational

MFC Mau Forest Complex

MRB Mara River basin

MR Mara River

MRWUA Mara River Water Users Association

NASA National Aeronautics and Space Administration NetCDF Network Common Data Format

NRB Nile River Basin PI Principal Investigator PRI Polarization Ratio Index PRI Precipitation Radar RfGS rainfall gauging stations RGS River gauging stations SMAP Soil Moisture Active Passive SMOS Soil Moisture and Ocean Salinity

SMOSMANIA Soil Moisture Observation System - Meteorological Automated Network Integrated Application

SRTM Shuttle Radar Topography Mission

SSM Surface soil moisture SWAT Soil Water Assessment Tool SWI Soil Water Index

TIFF Tagged Image File Format

TMI TRMM Microwave Imager

TMPA TRMM Multi-Satellite Precipitation Analysis

TRMM Tropical Rainfall Measurement Mission

TU Wien Vienna University of Technology

USDA United States Department of Agriculture

WRMA Water Resources Management Authority

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

1. INTRODUCTION

1.1. Background

Recent studies on the use of satellite observed soil moisture estimates in hydrological models have shown that these products have great potential in contributing to the quality of hydrological modelling results especially in poorly gauged catchments (Bolten et al., 2010; Brocca et al., 2010; Draper et al., 2011; Matgen et al., 2012; Pauwels et al., 2002; Scipal et al., 2008). Khan et al. (2012) in their study on microwave satellite modelling in Okavango basin (South Africa) found a Pearson correlation coefficient of 0.9 between measured runoff and Advanced Microwave Scanning Radiometer for Earth Observation System (AMSR- E) observed soil moisture. Scipal et al. (2005) in their study on soil moisture-runoff relationship at the catchment scale as observed with coarse resolution microwave remote sensing demonstrated that there is relevant hydrological information in course resolution satellite data. They used regression equation of the best fit relationship between ERS observed soil moisture and measured runoff to simulate runoff. Meier et al. (2011) in their study on hydrological real-time modelling in the Zambezi river basin further developed the concept by introducing rainfall as a forcing data. They built the model on the basis of the relationship found between satellite observed soil moisture, rainfall and in-situ measured runoff. From the soil moisture estimates, the catchments averaged profile soil moisture is calculated and expressed as Basin Water Index (BWI). Its values range from 0-1 with 0 signifying a completely dry basin with all the rainfall infiltrating, and 1 a completely saturated basin with constant infiltration. In this concept, BWI is used to partition rainfall into surface runoff and infiltration.

Some of the microwave remote sensing instruments which have provided soil moisture estimates at global scale include European Space Agency’s (ESA) Soil Moisture and Ocean Salinity (SMOS) mission, the European Remote Sensing (ERS) scatterometer and the Advanced Scatterometer (ASCAT) and National Aeronautics and Space Administration’s (NASA) Advanced Microwave Scanning Radiometer for Earth Observation System (AMSR-E). NASA is scheduled to launch the Soil Moisture Active Passive (SMAP) mission in 2014-2015. The instrument will have the capability of differentiating between frozen from thawed land surfaces (Entekhabi et al., 2010). Previous studies comparing retrievals from ASCAT and AMSR-E and ASCAT and SMOS indicate that ASCAT retrievals have better correlation with in-situ measurements (Brocca et al., 2011; Parrens et al., 2012). (Brocca et al., 2011) compared the soil moisture estimates generated from ASCAT and AMSR-E sensors with in-situ measurements in over 17 sites in Italy, Spain, France and Luxembourg. The authors used the Land Parameter Retrieval Model (LPRM), the Polarization Ratio Index (PRI) and the standard NASA algorithm to retrieve moisture data from the AMSR-E product. They used the Vienna University of Technology (TU Wien), change detection algorithm for retrieval from the ASCAT product. Out of the three sets of soil moisture estimates retrieved from the AMSRE-E product, the estimates by the LPRM had the highest correlation with in-situ measurements. Estimates from the ASCAT product had the best correlation results compared to estimates from the AMSRE-E products for approximately 5 cm soil layer. The average correlation coefficients were 0.71 and 0.62 for the ASCAT and the AMSR-E (retrieved using the LPRM), respectively. Parrens et al.

(2012) compared ASCAT and SMOS Surface Soil Moisture (SSM) products with Interaction-Soil-

Biosphere-Atmosphere (ISBA-A-gs) model simulations and in-situ measurements from the Soil Moisture

Observation System - Meteorological Automated Network Integrated Application (SMOSMANIA)

network. From their study, they found out that the significant anomaly correlation coefficients between in

situ measurements and the SMOS (ASCAT) product was in the range of 0.23 to 0.48 (0.35 to 0.96).

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1.2. Problem statement

MRB is a sub catchment of the Lake Victoria basin (LVB) and the larger Nile River Basin (NRB). In the upper parts of the basin is the Mau Forest Complex (MFC) where the Mara River (MR) originates from.

The forest is a key water tower, a source for other rivers including Sondu, Njoro and Ewaso Ng’iro rivers.

In the middle part of the catchment is the tropical savannah vegetation supporting the unique Mara- Serengeti ecosystem, famous with the scenic large scale seasonal migration of the wilder beast migration.

In the south western parts is the Mara Wetlands ecosystem. MR and its two main tributaries, Amala and Nyangores, are the only perennial rivers in the basin. The ecosystems, thriving tourism industry, agriculture and pastoral farming depend on these rivers especially during the dry seasons (Dessu et al., 2014; Gereta et al., 2009). According to Dessu and Mellesse (2012), a third of available arable land in MRB is under small scale farming.

Previous studies show that there has been change to the MR flow regime. A study on the impacts of land use/cover on the hydrology of MR by Mati et al. (2008) using Geospatial Stream Flow Model (GeoSFM) found out that the peak flows have increased by 7%, occurring 4 days early for the period between 1973 and 2000. Using Landsat images, they also found out change in land cover/use over the same period.

Notably, agricultural and wetland areas had increased by 203% and 387% while the savannah vegetation and forest areas were found to have reduced by 79% and 32% respectively. Mango et al. (2011) used the Soil Water Assessment Tool (SWAT) to investigate the impact of land use and climate on the hydrology of the upper MRB. Their results showed that conversion of forest areas to agriculture and grasslands areas was most likely reducing dry season flows while increasing quick peak flows. Human activity in MRB is affecting both the flow regime and the water quality of MR, (Gereta et al., 2009), (see also figure 1). Juston et al. (2013) used 44 year historical data to study the rating curve uncertainty and change in discharge time series of the Nyangores River. From 4 Flow Duration Curves (FDC) of 8 year data intervals, they detected a reduction in the lowest base flow.

There is need for integrated management of the basin’s water resources for it to meet the demand of the competing users especially during drought. To achieve this, hydrological models can be very useful to the managers. However as noted by Dessu and Mellesse (2012) in their study on modelling rainfall-run off processes in the MRB using SWAT, performance of the model in the basin depends on the quality and quantity of discharge data. They noted uncertainties in the discharge data. Previous studies indicate that lack of sufficient in-situ data, especially in developing countries, is a challenge to researchers, (Khan et al., 2012; Sivapalan, 2003). Globally, available in-situ data lacks homogeneity in the quality of individual

Figure 1: The picture on the left shows a man cutting trees in the upper Mara River Basin. The picture on the right shows men washing motorbikes and few steps down stream, cattle drinking the turbid water. Human activities are

contributing to degradation of the basin. Pictures by Vekerdy Z. (2013)

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

measurements as seen with for example, global soil moisture measurements, (Dorigo et al., 2011; Dorigo et al., 2013). In-situ measurements are in particular difficult and time consuming (Brocca et al., 2007;

Engman & Chauhan, 1995; Robock et al., 2000). This has motivated more research on derivation of hydrological information from satellite derived products.

This research builds from success of previous studies in runoff simulation models based on satellite observed soil moisture and rainfall products. The approach has shown to be very promising in addressing the problem of modelling data scarcity in poorly gauged basins. The satellite observed soil moisture and rainfall products used in this research are from ASCAT and Tropical Rainfall Measurement Mission (TRMM) respectively. The products are readily available in open source internet databases. The research is linked to the ESA Tiger Initiative - Alcantara Project No. 12-A15. It is expected to contribute towards flow estimation in the Lower Mara basin for wetlands hydrodynamic modelling by Joseph Mtamba – the PI.

1.3. Objectives

The main objective of this thesis is to use satellite based soil moisture and rainfall products for quantifying the runoff of the Mara River basin.

The specific objectives of the thesis are as follows:

x To develop an empirical model simulating Mara river runoff as function of the soil moisture using satellite observed rainfall as forcing data;

x To calibrate and validate the model for three gauging stations along the Mara river using satellite observed rainfall and soil moisture;

x To investigate the performance of the calibrated model for the different sub-catchments.

1.4. Research questions

The objectives defined above led to the following questions which this research sought to answer:

x Is there a relationship between satellite observed soil moisture and rainfall, and measured runoff of the Mara River?

x How do the model parameters behave for the different sub-catchments?

x How does the model performance compare for the different sub-catchments?

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2. STUDY AREA AND DATA COLLECTION

2.1. Study area

MRB covers an area of 13750 km

in south western Kenya and north western Tanzania. The MR originates from the MFC at an attitude of about 3000 metres above sea level (m.a.s.l). The river flows south westwards over a stretch of 395 km before draining into Lake Victoria at Musoma in Tanzania. It has two main perennial tributaries in the upstream part, namely the Nyangores and Amala rivers. Analysis of historical (1970 to 1996) discharge data from for Mara river at Mara mines, Nyangores at Bomet and Amala at Mulot shows a mean of 33.9 m

s

, 8.4 m

s

and 9.9 m

s

with standard deviation of 60 m

s

, 7.1 m

s

and 19.9 m

s

respectively (Dessu & Mellesse, 2012). The MRB has two rainy seasons. The long rainy season is between March and June and the short season is between November and December. The mean annual rainfall varies from 1000 mm to 1750 mm, 900 mm to 1000 mm and 300 mm to 800 mm in the upper, middle and lower parts of the basin respectively (Dessu et al., 2014; Dessu & Mellesse, 2012;

Krhoda, 2005). Figure 2 is a map showing the major land covers/uses in the basin. The map also shows the discharge gauging stations along Mara, Nyangores and Amala rivers. The middle areas of the catchment are dominantly savannah vegetation supporting the Mara-Serengeti ecosystem. On the lower parts of the basin are the Mara wetlands.

Figure 2: Map of the MRB. The major land covers/uses in the basin include forest reserves on the upper northern parts, in the middle parts are the savannah vegetation supporting the Mara-Serengeti ecosystem. In the lower

southern parts is Mara wetlands. Source: Dessu & Mellesse (2012)

2.2. Ground measurements and field observation

Fieldwork was undertaken between September 15 and October 8, 2013. The activity was partly funded by ESA Tiger Initiative. The objectives of the field work were to:

x Contact a reconnaissance of the study area

x Obtain runoff data

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

x Collect rainfall data

x Collect soil samples for soil characterisation

x Vegetation mapping in the Mara wetland for the ESA Tiger Initiative - Alcantara Project No. 12- A15.

The fieldwork team was composed of:

1. Jonathan Mwania - Master of Science student 2. Joseph Mtamba - PI

3. Dr Zoltan Vekerdy - Supervisor

The team traversed the basin collecting soil samples and making observations of the basins characteristics including land cover/use, topography and the RGSs beginning from the source of Nyangores and Amala and then downstream all the way to the Mara wetlands and to the outlet to Lake Victoria.

2.2.1. Runoff data

The runoff data is needed for validation and calibration of the soil moisture-runoff model. There are six river gauging stations (RGS) along the MR and its two main tributaries, Nyangores and Amala (see tables 1). Out of the six RGSs, only three have got long time series of data with minimal gaps. These are Mara mines, Nyangores and Amala. Data for these three RGS was collected from WRMA regional office in Kisumu, Kenya. The data are daily averages expressed in m3s-1. Historical data for Mara mines, Nyangores and Amala Mara-Lalgorian Bridge and Kirumi Ferry RGSs was obtained from the UNESCO – IHE courtesy of Professor M. E. McClain and Joseph Mtamba of the University of Dar Salaam.

Vandalism, negligence (see figure 3) and destruction of the RGS equipment by floods, were noted as the causes of gaps in the runoff data of the Mara River. The Nyangores and Amala RGSs were rehabilitated and installed with automatic gauges in 2012. However the data used in this research is for up to June 2011.

At the Mara Mines, Nyangores and Amala RGS, two readings of the water level are taken daily, one in the morning and the other in the evening. Rating curves are then used to estimate daily average discharges. In Mara mines a new rating curve was developed in 2012. However all the data for this station used in this research is for the period before the new curve was developed. Inconsistency on the time for recording the morning and evening water levels by the gauge readers was noted as a possible source of uncertainty in

with an automatic gauge with support from the World Bank Nile Basin Initiative (WB-NBTF), Swedish International Development Cooperation Agency (SIDA) and the Germany Society for International cooperation (GIZ). The picture on the right is neglected RGS at Emarti bridge along the Amala river. Picture by: Vekerdy Z.

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the data. During fieldwork, it was also observed that the Mara mines RGS was incapable of capturing extreme flood events. This is because the water levels surpass the gauge staff height. The river cross sectional dimension at the location may change with time as they are not embanked.

Table 1: RGS along the Mara River. Only the Mara mines, Nyangores and Amala RGSs have relatively long historical data.

Station Name Station code

Longitude (

E)

Latitude (

S)

Altitude (masl)

Start Year

Nyangores 1LA03 35.35 -0.79 1899 1963

Amala 1LB02 35.43 -0.89 1860 1955

Lalgorian bridge ILA04 35.04 -1.23 1594 1970

Mara Mine 5H2 34.55 -1.55 1181 1969

Kirumi ferry 5H3 33.86 -1.51 1132 1969

2.2.2. Rainfall data

The in situ rainfall data was used to investigate the reliability of the satellite rainfall product. There are forty four rainfall gauging stations (RfGS) within and around the basin (see also figure 2). Data for the stations on the Kenyan side of the basin was obtained from KMD, Nairobi. For the stations on the Tanzanian side, the data was provided by Joseph Mtamba of University of Dar Salaam. Out of the forty four stations, only six (shown in figure 6) had sufficient data falling within the span of satellite rainfall data used in this research. Sample RfGS visited during the field work were observed to have the tipping bucket type of gauges (see also figure 4 below).

Figure 4: Weather station at the Mara River Water Users Association (MRWUA) office in Mulot. The station has a tipping bucket and a manual rain gauge. The weather station automatic measuring instruments are not yet connected

to the data logger. Picture by Vekerdy Z. (2013) 2.2.3. Soil characterisation

Fifteen soil samples were collected from a depth of 0-20cm during the fieldwork. These samples, in

addition to nine others collected in a previous fieldwork by Joseph Mtamba were used for particle

distribution analysis. The analysis was conducted at the University of Dar Salaam in Tanzania. The results

of the analysis were used to classify the soils as suggested by United States Department of Agriculture,

USDA (1999). Additional soil data was extracted from the Harmonized World Soil Database (HWSD)

(FAO et al., 2012) and used to identify the soil types with respect to the classifications (table 2). Figure 5

shows soil map of the MRB extracted from the 1:5 million HWSD raster map including the soil sampling

points for this research. The results of the analysis helped in understanding the modelling results.

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

Table 2: Soil particle distribution analysis results, S Pt. is sample point, C is clay, Slt silt, Snd sand and G gravel. The samples were classified with the USDA Texture Class.

Pt S ^Long.

E Lat.

0

N C

% Slt

% Snd

% G

% USDA

Texture Class HWSD Soil type

1 35.51 -0.87 17 55 26 27 loam Humic Cambisols (CMu)

2 35.50 -0.87 17 49 34 0 clay loam Haplic Phaeozems (PHh)

3 35.54 -0.82 14 39 35 12 clay (light) Mollic Andosols (ANm) 4 35.57 -0.77 10 48 18 24 clay (light) Mollic Andosols (ANm) 5 35.52 -0.77 13 46 39 2 clay (light) Mollic Andosols (ANm) 6 35.45 -0.81 18 52 27 3 clay (light) Mollic Andosols (ANm) 7 35.41 -0.96 13 67 18 2 silty clay Vertic Luvisols (LVv)

8 35.23 -1.06 14 32 49 5 silt Eutric Vertisols (VRe)

9 35.42 -0.71 10 42 46 2 clay (light) Mollic Andosols (ANm) 10 35.33 -0.83 13 53 34 0 sandy clay Luvic Phaeozems (PHl)

11 35.25 -0.93 23 51 26 0 silt Eutric Vertisols (VRe)

12 35.25 -1.08 4 33 57 6 sandy clay Luvic Phaeozems (PHl)

13 35.24 -1.17 10 47 41 2 silt Eutric Vertisols (VRe)

14 35.20 -1.18 10 44 41 5 silt Eutric Vertisols (VRe)

15 35.12 -1.20 10 53 35 2 silt Eutric Vertisols (VRe)

16 34.28 -1.47 19 58 23 0 loamy sand Eutric Fluvisols (FLe) 17 34.12 -1.65 12 35 53 0 silty clay loam Eutric Planosols (PLe) 18 34.26 -1.58 15 63 22 0 silty clay loam Eutric Planosols (PLe) 19 34.57 -1.52 5 37 56 3 silty clay loam Eutric Planosols (PLe) 20 34.51 -1.50 13 59 28 0 silty clay loam Eutric Planosols (PLe) 21 34.63 -1.55 6 38 54 2 silty clay loam Eutric Planosols (PLe) 22 34.87 -1.57 6 46 45 4 silty clay loam Eutric Planosols (PLe)

23 34.68 -1.66 5 37 56 3 sandy clay Luvic Phaeozems (PHl)

24 34.71 -1.74 5 36 59 0 sandy clay Luvic Phaeozems (PHl)

2.3. Satellite data sets

The satellite data sets used in this research were:

1. TRMM rainfall

2. ASCAT Soil Water Index (SWI).

3. Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) All these data sets were downloaded from open source internet data bases (see also table 3)

Table 3: Satellite data sources - the sources are open to the public.

Data Web Source

TRMM rainfall http://mirador.gsfc.nasa.gov/cgi-bin/mirador/homepageAlt.pl?keyword=TRMM ASCAT SWI http://rs.geo.tuwien.ac.at/products/

SRTM DEM https://lta.cr.usgs.gov/SRTM2

The satellite soil moisture product to be used in this model is the Soil Water Index (SWI). The product is

derived from scatterometer generated SSM following the concept of a two-layer force-restore model as

18

suggested by Wagner et al. (1999b). In this model, the profile soil moisture is calculated from previous SSM measurements as a function of time and expressed as the SWI as shown in equation 1 below. This model was developed at the Vienna University of Technology (TU Wien).

ܹܵܫ ൌ

షሺ೟ష೟೔ሻ

೅

σ ௘೙ ^{షሺ೟ష೟೔ሻ}೅

೔

݂݋ݎݐ ൌ ݐ݅ ൏ ݐ (1)

Where SSM is the surface soil moisture from scatterometer at time –

 is the characteristic time length. The SSM measurements are generated using a change detection algorithm described in (Wagner et al., 1999a)

The SWI product used in this research is calculated from ASCAT sensor generated SSM data distributed by European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). ASCAT is a remote sensing instrument on board Meteorological Operational (MetOp) platform. The instrument is an active microwave with vertical polarization and C-band at 5.255 GHz (Brocca et al., 2010; Wagner et al., 2013). It is a follow up to the ERS scatterometer. (Brocca et al., 2011; Brocca et al., 2010; Wagner et al., 2013)

The product was developed under the framework of the Geoland2 project. It has a daily temporal resolution and 12.5 km spatial resolution. It is available for the period from 1

January 2007 up to date. It is in Hierarchical Data Format (HDF5) and compressed in .bz2. After downloading the product it was pre-processed using Interactive Data Language (IDL) codes (see appendix A and B). The data was extracted for further processing using BEAM VISAT software.

2.3.2. Tropical Rainfall Measurement Mission (TRMM) rainfall

TRMM rainfall data was used as a forcing data to the rainfall-runoff model in this research. TRMM is a joint mission of NASA and Japan Aerospace Exploration Agency for measuring tropical and subtropical rainfall. The mission employs various instruments including TRMM Microwave Imager (TMI), Cloud and Earth Radiant Energy Sensor (CERES), Precipitation Radar (PR) and Lightning Imaging Sensor (Liu et al., 2012; NASA, 2011). The TRMM satellite observations validation with ground observations is supported by the TRMM Ground Validation (GV) program at the NASA/ Goddard Space Flight Canter (GSFC) (NASA, 2011; Wolff et al., 2005). TRMM provides several rainfall products (see table 4). The data range of the TRMM product is from 1

January 1997 up to date.

Table 4: Gridded TRMM rainfall products have been spatial averaged with a resolution of 0.25° x 0.25° and 1° x 1°.

3B42 is also available on a daily temporal resolution. Source: NASA (2011)

Gridded TRMM Products

Product ID Product Name

3A11 Monthly 5° x 5° Oceanic Rainfall

3A12 Monthly 0.5° x 0.5° mean 2A12, profile, and surface rainfall 3A25 Monthly 5° x 5° and .5° x .5° Space-borne Radar Rainfall 3A26 Monthly 5° x 5° Surface Rain Total

3B31 Monthly 5° x 5° Combined Rainfall 3A46 Monthly 1° x 1° SSM/I Rain

3B42 3-hour 0.25° x 0.25° TRMM and Other-GPI Calibration Rainfall 3B43 Monthly TRMM and Other Sources Rainfall

CSH Monthly 0.5° x 0.5° Convective & Stratiform Heating

This research used the 3B42 version 7 product resampled to daily temporal resolution. The product is a

result of the TRMM Multi-Satellite Precipitation Analysis (TMPA) (NASA, 2011). The data is available on

a 0.25° x 0.25° resolution and at latitudes 50° N and 50° S.

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

The data was downloaded in Network Common Data Format (NetCDF). IDL codes (see appendix C and D) were used to convert the data into Tagged Image File Format (TIFF) and then into American Standard Code for Information Interchange (ASCII) file which was then opened in excel spread sheet for further processing.

2.3.3. Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM)

This research used the SRTM DEM with a 90m spatial resolution (3arc seconds). The DEM has been resampled using cubic convolution and voids filled using interpolation algorithms and other sources of elevation data (USGS, 2012). DEM product specifications are elaborated in table 5. The DEM was downloaded via Earth explorer as Geo-referenced TIFF (GeoTIFF). It was processed using arc hydro toolbox in arc map. The delineation was done for Mara mines, Nyangores and Amala sub-catchments with respect to their corresponding RGSs. The area of the sub catchments were established as 11,280, 693 and 697km

for Mara mines, Nyangores and Amala sub-catchments, respectively. Figure 6 shows the delineated catchments and the drainage network. The sub catchment shape files were used in masking the satellite observed soil moisture and rainfall products for data extraction. The DEM indicates the highest and the lowest point in the basin to be 3063 m.a.s.l. and 1134 m.a.s.l. respectively, (see also figure 6).

Table 5: SRTM DEM specifications, source: USGS (2012) Product Specifications

Projection Geographic

Horizontal Datum WGS84

Vertical Datum EGM96 (Earth Gravitational Model 1996)

Vertical Units Meters

Spatial Resolution 1 arc-second for the United States (~30 meters) 3 arc-seconds for global coverage (~90 meters) Raster Size 1 degree tiles

C-band Wavelength 5.6 cm

20

Figure 5: Soil Map of the MRB extracted from the HWSD raster map. The sampling points for this research are also shown in the map.

Figure 6: Processed SRTM DEM illustrating the elevation of MRB. The figure also shows the RfGS used in this research and RGS along the MR

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

3. SWI, RUNOFF, RAINFALL TIME SERIES ANALYSIS

The SWI used in this research has been derived from ASCAT generated SSM. From this SWI, Basin Water Index (BWI) index is calculated as suggested by Scipal et al. (2005). They defined BWI as SWI averaged over a given catchment, see equation 2.

ܤܹܫ ൌ

௡

(2) Where n is the number of pixels in the catchment and i refers to a pixel (-). BWI is dimensionless and varies from 0 to 1. A BWI value of 0 indicates completely dry catchment condition, while a value of 1 indicates a completely saturated condition. BWI daily time series data sets for the three sub-catchments namely Mara mines, Nyangores and Amala were calculated. Ground soil moisture measurements were not available for validation of the BWI. TRMM rainfall daily time series for each of the three sub-catchments were calculated by averaging the extracted TRMM data over the whole catchment. Figure 7 shows BWI, TRMM and discharge 30 day daily mean time series plots for the three sub catchments. The BWI and TRMM data sets are from January 2007 up to July 2013. There are a lot of gaps on the discharge data sets.

Figure 7: BWI, TRMM and discharge 30 day daily mean time series plots for Mara mines, Nyangores and Amala sub catchments. BWI is expressed as a percentage on the right Y axis together with rainfall in mm while runoff is on the left scale. Nyangores and Amala have relatively higher BWI compared to Mara mines. The peaks tend to follow a

seasonal pattern. The peak rainfall seasons in MRB are March to May and November to December.

22

Also in this figure, the peaks of the BWI, TRMM and runoff are shown to coincide. However there is a notable exceptional case of the peak events in 2010 for Amala sub-catchment. In this case, the runoff is shown to peak before BWI. Nyangores and Amala have relatively high and low BWI peaks compared to Mara mines. For the period of under consideration, Nyangores had the highest mean BWI of 0.46 and a standard deviation of 0.2 followed by Amala with mean of 0.45 and a standard deviation of 0.2. Mara mines had the lowest mean of 37 with a standard deviation of 16. From figure 9, a seasonal trend is seen with the peaks coinciding with the rainfall seasons in the MRB. The basin has two rain seasons between March and June and between November and December.

3.1. BWI and TRMM rainfall relationship

The relationship between BWI and TRMM was further investigated quantitatively using the coefficient of determination (R

). 30 day daily mean time series for the three sub-catchments were used in this investigation. Temporal averaging of the data sets was done to minimise noise. The period for the investigation was between January 2007 and July 2013. The best fitting trend line for BWI plotted against TRMM was found to be logarithmic (figure 8). The R

values for Mara mines, Nyangores and Amala sub- catchment were 0.54, 0.5 and 0.51 respectively. From figure 8, it can be seen that as BWI and rainfall increases, the scatter of the data points increases also. This is because as the rainfall increases, soil moisture continues increasing until the soil is completely saturated (BWI = 1). At this point, infiltration is at maximum capacity and any further increase in rainfall intensity leads to increase in contribution to surface runoff. This supports the findings of Meier et al. (2011) who however suggest that soil moisture is more correlated to occurrence of rainfall events than to the magnitude of the rainfall event. This latter was not investigated in this research.

Also in figure 8, a distinct difference in the slope of the trend line for Mara mines compared to Nyangores and Amala is observed. The Mara mines slope is gentle compared to the rest. .

The shape of the trend line can be assumed to be related to catchment characteristics influencing infiltration. From these curves, it can thus be deduced that there is higher infiltration in Nyangores than in Amala with Mara mines having the lowest. These results support the arguments by previous studies which attribute the high infiltration in Nyangores and Amala to their relatively higher forest cover compared with

Figure 8: BWI versus TRMM scatter plots forMara mines, Nyangores and Amala sub catchments. The plots are for 30 day daily means. The slope is taken as an indicator of the infiltration rate of the given catchment. A

steep slope indicates higher infiltration rate and vice versa. Mara mines is shown to have the lowest infiltration rate compared to Nyangores and Amala. The study period was between January 2007 and July

2013.

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

Mara mines (Dessu et al., 2014; Dessu & Mellesse, 2012; Gereta et al., 2009; Mango et al., 2011; Mati et al., 2008).

3.2. BWI and runoff relationship

The relationship between BWI and runoff was investigated quantitatively using R

. Runoff 30 day daily mean time series for the three sub-catchments were plotted against BWI. The best fitting trend line for this relationship was found to be exponential with R

values of 0.6, 0.68 and 0.67 for Mara mines, Nyangores and Amala respectively. The period for the investigation was between January 2007 and July 2013. From figure 9 it can be seen that the scatter of the data points increases with increase of BWI and runoff. The explanation to this trend is that, as the soil moisture increases surface runoff also increases and as the moisture content approaches saturation point, infiltration rate approaches optimal level with more rainfall being routed to surface runoff. Meier et al. (2011) and Scipal et al. (2005) in a similar analysis found similar behaviour in the relationship of BWI and runoff. Meier et al. (2011) attributed this decoupling of soil moisture from runoff as the moisture content approaches saturation point to rainfall.

From figure 9 it can be seen that the slope of the trend lines for Mara mines and Amala are steeper compared to that of Nyangores. The steepness can be taken to indicate the area related storage capacity with very steep slope indicating low storage capacity. With this assumption, Mara mine is shown to have lower storage capacity compared to the other sub catchments. Comparing Nyangores and Amala, Amala is shown to have a steeper slope as BWI increases. Amala is also shown to have a relatively gentle slope for lower BWI compared to Nyangores. This may be an indication of lower flow rates during dry seasons in comparison to Nyangores. These results support the findings by previous studies that Nyangores and Amala have higher storage capacities which serves to sustain Mara river during dry seasons, (Dessu et al., 2014; Dessu & Mellesse, 2012; Mango et al., 2011; Mati et al., 2008).

3.3. TRMM rainfall versus in situ measured rainfall

TRMM data was validated by investigating its relationship with the in-situ rainfall measurements. The investigation was performed through comparison of TRMM and in-situ measured 30 days summations on a pixel to point measurement basis for selected RfGSs in the MRB. The period for the investigation was between January 2007 and July 2013. R

and Root Meat Square Error were used to assess the relationship.

The number of RfGSs with sufficient data and their spatial distribution (see also figure 6) was not

for 30 day daily means. The steepness of the slope is taken to indicate the water storage capacity of the catchment. A steep slope indicates low catchment storage capacity and vice versa. Nyangores is shown to have

the highest storage capacity. The study period was between January 2007 and July 2013.

24

sufficient for conducting a conclusive spatially averaged comparison. Only six RfGSs were considered for this analysis. 30 day summations were used so as to smooth the high spatial-temporal variability. MRB being in the tropics has intense but less spatially distributed rainfall events. For all the six stations, a linear relationship was found. The R

and RMSE varied from 0.5 to 0.86, and 47.7 mm/30 days to 73.7 mm/30 days respectively (see table 6). Ilkerin Integral Development Project RfGS (09135025) had the highest R

(0.86) and lowest RMSE (29.8 mm/30 days). However the results for this RfGS were not considered conclusive since very few points were used for the analysis. Governor’s Camp RfGS (09135026) had the highest RMSE of 73.7mm/30 days despite having a high R

. The Olenguruone D.O's Office - Molo (09035085) and Tenwek Mission RfGS (09035079) were observed to be systematically underestimating rainfall with the rest overestimating with respect to a 1:1 linear relationship with TRMM estimates, (figure 10). These results indicate the uncertainty brought by lack of homogeneity in the quality of the RfGS.

Previous TMM validation studies have shown that TRMM fairly estimates rainfall. Wolff et al. (2005) in their research to analyse TRMM with tipping bucket rain gauges over central Florida, found out that the correlation was better on monthly and yearly scales than on shorter time scales. They attributed the low correlation on shorter time scales to the difference in spatial and temporal sampling modes.

Prasetia et al. (2013) in their research on validation of TRMM estimates in the region over Indonesia conducted a similar investigation and found out that there was a medium correlation between the TRMM and in-situ measurements. Prakash and Gairola (2013) in their research on TRMM rainfall validation over the tropical Indian ocean with measured rainfall on a daily time scale also found good correlation with RMSE varying from 1 to 22 mm d

.

Figure 10: TRMM versus in-situ measured rainfall for selected RfGS scatter plots. The data plotted is pixel (TRMM) to in-situ measurements computed to 30 day summations. The solid line represents the linear relationship of TRMM and in-situ measurement while the dotted line represents a 1:1 linear relationship. The period for the investigation was

between January 2007 and July 2013.

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

Table 6: TRMM rainfall validation with in-situ measured rainfall. The period for the investigation was between January 2007 and July 2013. There are gaps in the in-situ measurements for all the RFGS in the basin.

Station Name Station

Code

Location

No of points r

RMSE of 30 summations day

(mm) Latitude

o

S Longitude

o

E

Tenwek Mission – Sotik 09035079 -0.75 35.37 26 0.66 47.7

Olenguruone D.O's Office –

Molo 09035085 -0.58 35.68 37 0.52 57.8

Bomet Water Supply 09035265 -0.78 35.35 93 0.52 51.7

Oltome Green Lodge –

Narok 09135004 -1.07 35.52 23 0.50 69.2

Ilkerin Integral Development

Project 09135025 -1.78 35.70 12 0.86 29.8

Governor's Camp 09135026 -1.28 35.03 24 0.83 73.7

3.4. Water budgets at Mara mines, Amala and Nyangores

Annual water budgets at Mara mines, Amala and Nyangores sub catchments were calculated from 1998 up to 2012 (see table 7). The rainfall summations were calculated from the TRMM time series data sets.

Evapotranspiration (ET) was calculated as residual from rainfall and runoff. A lot of gaps were noted in the runoff data as from 1990 especially on the Mara Mines RGS. This made it difficult to account for runoff in each year hence only a non-conclusive analysis could be performed. Historical data for Nyangores and Amala rivers were used to analyse the seasonal runoff trend. Figure 11 shows the monthly mean runoff for Nyangores and Amala rivers for the period 1964 to 1992. From this figure it is shown that Amala River has a higher and early peak runoff than Nyangores. It is also shown that Nyangores has higher base flow compared to Amala. Two distinct peak runoff seasons corresponding to the MRB wet season can also be observed.

Surprisingly, for the period under consideration, Mara mines has a higher mean annual TRMM rainfall of 1403 mm compared to Amala which has an annual mean of 1360 mm with a standard deviation of 148 mm and 178 mm respectively. Nyangores was found to have the highest mean annual TRMM rainfall with a standard deviation of 196mm.

0 5 10 15 20 25

J F M A M J J A S O N D

Runoff (m3/s)

Month

Nyangores River Amala River

Figure 11: Monthly mean runoff for Nyangores and Amala rivers for the period 1964 to 1992. The Amala River has higher and early peak runoff compared to Nyangores. The latter however has higher base flow

26

Table 7: Water budgets for Mara mines, Nyangores and Amala sub catchments. There are many gaps in the runoff data hence these budgets are not conclusive

Runoff annual summations (mm/year)

TRMM Rainfall annual summations (mm/year)

ET annual summations - Residue (mm/year) Year Mara

mines

Nyangores Amala Mara mines

Nyangores Amala Mara mines

Nyangores Amala

1998 668 1290 1405 1320 1290 737

1999 380 113 1374 1416 1250 1036 1137

2000 192 94 1243 1247 1083 1055 989

2001 632 406 1426 1581 1430 949 1024

2002 395 314 1473 1558 1416 1163 1102

2003 509 1319 1448 1314 939

2004 370 185 1294 1371 1216 1001 1031

2005 254 415 392 1178 1270 1132 924 855 740

2006 355 465 1681 1921 1682 1326 1456

2007 628 882 1581 1765 1580 1137 698

2008 413 1422 1561 1402 1148

2009 129 1214 1273 1105 1144

2010 598 1459 1703 1518 861

2011 1586 1661 1503

2012 1505 1611 1448

Mean 403 433 341 1403 1519 1360 1100 1052 960

Max 598 668 882 1681 1921 1682 1326 1456 1137

min 254 129 94 1178 1247 1083 861 737 698

Std.

dev.

177 165 270 148 196 178 242 182 173

RUNOFF MODELLING OF THE MARA RIVER USING SATELLITE OBSERVED SOIL MOISTURE AND RAINFALL

4. RAINFALL-RUNOFF MODEL

For this research, the conceptual lumped soil moisture-runoff model by Meier et al. (2011) is used. The model includes two linear storage reservoirs, namely surface and subsurface storage layer. The inputs to this model are BWI and satellite rainfall data. This model does not account for catchment heterogeneity and land use/cover (Meier et al., 2011). The concept of the model is that BWI is the state variable directing rainfall into surface and groundwater runoff production pathways. This relationships is expressed as follows,

ܫ

ൌ ݇

ܣܴሺݐሻ൫ͳ െ ܤܹܫሺݐሻ൯ (3)

Where, I

is the infiltration to the subsurface storage (m

d

), A is the area of the catchment (km

), R is the rainfall (mm d

), 

is a model parameter (d

) and t is the model time step (d). As the soil becomes more saturated, more rainfall is routed through surface storage. Similarly as the soil becomes less saturated, less rainfall is routed through subsurface storage.

The change in surface and groundwater storage over a time step is calculated as follows,

οௌ_ೞሺ௧ሻ

ο௧

ൌ ݇

ܣܴሺݐሻܤܹܫሺݐሻ െ ܫ

െ ݇

ܵ

ሺݐ െ ͳሻ (4)

οௌ_ಸೈሺ௧ሻ

ο௧

ൌ ƒšሺܫ

൅ ݇

ሺܤܹܫሺݐሻ െ ܤܹܫሺݐ െ ͳሻǢ Ͳሻ െ ݇

ܵ

ሺݐ െ ͳሻ (5)

Where, S

and S

are the surface and subsurface storage components, respectively (m

d

), ∆S

and ∆S

are the change in surface storage and subsurface storage components, respectively (m

d

).

These surface and groundwater storage change equations are linked to their respective water budget as follows,

ܵ

ሺݐሻ ൌ

൅ ܵ

ሺݐ െ ͳሻ (6)

ܵ

ሺݐሻ ൌ

ο௧

൅ܵ

ሺݐ െ ͳሻ (7) The runoff components are subsequently computed from the storage components as follows,

ܳ

ሺݐሻ = ݇

ܵ

ሺݐ െ ͳሻ (8)

ܳ

ሺݐሻ = ݇

ܵ

ሺݐ െ ͳሻ (9)

Where, 

and 

are the surface and groundwater runoff components respectively. Summing the two components and routing provides the total runoff production,

ܳሺݐሻ ൌ ܳ

ሺݐ െ ο߬

ሻ ൅ ܳ

ሺݐ െ ο߬

ሻ (10)

Where,  is the total runoff (m

d

), ∆τ

This set of equations is schematically represented in Figure 12.

28

Figure 12: The input in this set up is rainfall. The level of BWI determines the distribution of rainfall between the surface and subsurface storage compartment. As the BWI increases, infiltration reduces and more rainfall is routed to

the surface storage. The two storage compartments contribute to surface and groundwater runoff. Source: Meier et al. (2011)

The physical meaning of the empirical parameters as described by (Meier et al., 2011) are: 

parameterizes the initial loss of rainfall due to evaporation and interception (d

); 

parameterizes the retention of water in the surface storage before being routed to the river (d

); 

quantifies retention of water in the surface storage before being transported to the subsurface storage (d

); and 

is the rate of depletion from the subsurface storage to the river (m

d

). The 

parameters are dependent on soil infiltration properties and catchment average retention time that is influenced by topography, geography and vegetation. According to Meier et al. (2011), ∆τ

are dependent on the size of catchment, but from equations (4-10) the uniqueness with respect to 

and 

is not clear.

In this research, the Meier et al. (2011) model has been modified by replacing the delay factor with a low pass filter approach. The low pass filter attenuates the storage components as a function of time before they are routed as runoff, as shown in equations 11 and 12. In this new approach, the contribution of previous rainfall events is factored. The reasoning is that contribution of a particular rainfall event is not instantaneous but rather increases exponentially over a given time before reaching a peak value. The total runoff is consequently computed as shown in equation 13.

Where:

ܳ

ሺݐሻ =

೔సሺ೟షభሻ

(11)

ܳ

ሺݐሻ =

σ^೙_{೔సሺ೟షభሻ}௘^{షሺ೟ష೔ሻ ഓ೒ൗ}

(12)

ܳሺݐሻ ൌ ܳ

ሺݐሻ ൅ ܳ

ሺݐሻ (13)

Where τ and τ

are the characteristic catchment response times (d) related to the surface and groundwater

runoff respectively.